Movie Theatre A has a popcorn machine with a 100-gallon capacity, and sells 3 gallons of popcom per hour. Movie Theatre B has a popcom machine with a 150-gallon capacity, and sells 5 gallons of popcorn per hour. Write an equation to show when the two popcom machines will have the same amount of popcom left. Use x as your variable (1 point)

Question

100 - 3x = 150 - 5x

3x - 100 = 5x - 150

100 + 3x = 150 + 5x

150 + 3x = 100 + 5x

Answer 1

To find the equation that shows when the two popcorn machines will have the same amount of popcorn left, we start by expressing the amount of popcorn left for each theatre in terms of the variable \( x \), which represents the number of hours passed.

For Movie Theatre A:

• Initial capacity: 100 gallons
• Sells 3 gallons per hour
• Amount left after \( x \) hours: \( 100 - 3x \)

For Movie Theatre B:

• Initial capacity: 150 gallons
• Sells 5 gallons per hour
• Amount left after \( x \) hours: \( 150 - 5x \)

We set the two expressions equal to each other to find when they will have the same amount of popcorn left:

\[ 100 - 3x = 150 - 5x \]

This is the correct equation that represents when the two popcorn machines will have the same amount of popcorn left.